When you receive Battle Items and Loot in the game, a notification will pop up (or if you are not in the game, when you log in) detailing each item that you have received.

In case you missed the pop-up notification before seeing the items that you have received, you can also check by:

Tapping the Menu icon > Inventory icon

A red circle will appear above the Inventory icon which shows a number. This corresponds to the amount of new items you have received. All new content (not previously in the inventory) in the Inventory are highlighted by the glowing 'New' notification.

Please note - if you already had the items received, you will not see the "New" notification above the item.